"Logarithmic Function" Exponential Function and Logarithmic Function PPT Courseware (Differences in Growth of Different Functions in Lesson 3)

Description

"Logarithmic Function" Exponential Function and Logarithmic Function PPT Courseware (Differences in Growth of Different Functions in Lesson 3)

Part One: Learning Objectives

1. Understand the meaning of linear rise, exponential explosion, and logarithmic growth. (emphasis)

2. Distinguish the differences in the growth rates of exponential functions, logarithmic functions and linear functions. (easy to mix)

3. Be able to choose appropriate function models to analyze and solve some practical problems. (difficulty)

core competencies

Cultivate the literacy of mathematical operations and mathematical modeling with the help of the growth characteristics of the three function models.

Logarithmic function PPT, part 2: independent preview and exploration of new knowledge

A preliminary exploration of new knowledge

Properties of the three functional models

First try

1. It is known that the variable y=1+2x, when x decreases by 1 unit, the change of y is ()

A． y decreases by 1 unit

B． y increases by 1 unit

C. y decreases by 2 units

D. y increases by 2 units

2. Among the following functions, the one that increases as x increases and is the fastest is ()

A． y=ex

B． y＝lnx

C. y=2x

D. y=e-x

3. The functional relationship between the total output C of a certain product in a factory over the past 8 years and time t (year) is as shown in the figure.

The following four statements:

①The output growth rate in the first three years is getting faster and faster; ②The output growth rate in the first three years is getting slower and slower; ③The production of this product stops after the third year; ④The output remains unchanged after the third year.

Among them, the correct serial number is _________.

Logarithmic function PPT, the third part: cooperative exploration to improve literacy

Differences in growth among several types of function models

[Example 1] (1) Among the following functions, the one with the fastest growth rate is ()

A． y=2 019x　B． y＝2019

C. y=log2 019x D. y＝2019x

(2) The following statement about the decrease of functions f(x)=log12x, g(x)=12x and h(x)=-2x in the interval (0, +∞) is correct ()

A． f(x) decreases faster and slower, g(x) decreases faster and faster, h(x) decreases slower and slower

B． f(x) decreases faster and faster, g(x) decreases faster and slower, h(x) decreases faster and faster

C. The decreasing speed of f(x) is getting slower and slower, the decreasing speed of g(x) is getting slower and slower, and the decreasing speed of h(x) remains unchanged.

D. f(x) decreases faster and faster, g(x) decreases faster and faster, h(x) decreases faster and faster

(1)A　(2)C　(1) The exponential function y=ax shows explosive growth when a>1, and as the value of a increases, the growth rate becomes faster, so A should be selected.

(2) Observe the images of functions f(x)=log12x, g(x)=12x and h(x)=-2x in the interval (0, +∞) (as shown in the figure):

The graph of function f(x) decreases faster in the interval (0,1), but the decrease speed gradually becomes slower; in the interval (1, +∞), the decrease becomes slower and slower. Similarly, the function The graph of g(x) decreases slowly in the interval (0, +∞), and the decreasing speed becomes slower and slower; the graph of function h(x) decreases at the same speed. ]

regular method

Common function models and growth characteristics

1Linear function model

The growth characteristic of the linear function model y＝kx＋bk>0 is a straight rise, and its growth rate remains unchanged.

2 Exponential function model

The growth characteristic of the exponential function model y=axa>1 is that as the independent variable increases, the function value increases faster and faster, that is, the growth rate is sharp, which is vividly called "exponential explosion".

3 logarithmic function model

The growth characteristic of the logarithmic function model y=logaxa>1 is that as the independent variable increases, the function value increases slower and slower, that is, the growth rate is gentle.

Class summary

Straight up, exponential explosion, logarithmic growth

For the straight line y=kx+b (k≥0), the exponential function y=ax (a>1), and the logarithmic function y=logbx (b>1), when the independent variable becomes very large, the exponential function grows more than the linear function. Fast, the linear function grows faster than the logarithmic function, and rises linearly, and its growth amount is fixed.

Logarithmic function PPT, the fourth part: reaching the standard in class and solidifying the double base

1. Thinking and analysis

(1) The function y=2x grows faster than y=2x. ()

(2) When a>1, n>0, in the interval (0, +∞), for any x, logax

(3) The function y=log12x decays slower and slower. ()

2. Among the following functions, the one with the fastest growth rate as x increases is ()

A． y=1

B． y=x

C. y=3x

D. y=log3x

3. If someone invests x yuan and makes a profit of y yuan, there are three options: A: y=0.2x, B: y=log2x+100, C: y=1.005x, then when investing 500 yuan, 1,000 yuan, and 1,500 yuan, you should choose the ________ plan respectively.

Keywords: Free download of PPT courseware for compulsory course 1 of Mathematics of High School People's Education A version, logarithmic function PPT download, exponential function and logarithmic function PPT download, difference in growth of different functions PPT download, .PPT format;

For more information about the PPT courseware "The Difference in the Growth of Different Functions between Exponential and Logarithmic Functions and Logarithmic Functions", please click the Difference in Growth of Different Functions ppt between Exponential Functions and Logarithmic Functions ppt Logarithmic Function ppt tag.

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Update Time: 2024-10-02

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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